{"id":"https://openalex.org/W2407031230","doi":"https://doi.org/10.1145/2890502","title":"Hybrid Montgomery Reduction","display_name":"Hybrid Montgomery Reduction","publication_year":2016,"publication_date":"2016-05-23","ids":{"openalex":"https://openalex.org/W2407031230","doi":"https://doi.org/10.1145/2890502","mag":"2407031230"},"language":"en","primary_location":{"id":"doi:10.1145/2890502","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2890502","pdf_url":null,"source":{"id":"https://openalex.org/S136160450","display_name":"ACM Transactions on Embedded Computing Systems","issn_l":"1539-9087","issn":["1539-9087","1558-3465"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Embedded Computing Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085541661","display_name":"Hwajeong Seo","orcid":"https://orcid.org/0000-0003-0069-9061"},"institutions":[{"id":"https://openalex.org/I3005327000","display_name":"Institute for Infocomm Research","ror":"https://ror.org/053rfa017","country_code":"SG","type":"facility","lineage":["https://openalex.org/I115228651","https://openalex.org/I3005327000","https://openalex.org/I91275662"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Hwajeong Seo","raw_affiliation_strings":["Institute for Infocomm Research, Singapore"],"affiliations":[{"raw_affiliation_string":"Institute for Infocomm Research, Singapore","institution_ids":["https://openalex.org/I3005327000"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100462347","display_name":"Zhe Liu","orcid":"https://orcid.org/0000-0001-8578-2635"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Zhe Liu","raw_affiliation_strings":["University of Waterloo, Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065515042","display_name":"Yasuyuki Nogami","orcid":"https://orcid.org/0000-0001-6247-0719"},"institutions":[{"id":"https://openalex.org/I163770644","display_name":"Okayama University","ror":"https://ror.org/02pc6pc55","country_code":"JP","type":"education","lineage":["https://openalex.org/I163770644"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yasuyuki Nogami","raw_affiliation_strings":["Okayama University, Japan"],"affiliations":[{"raw_affiliation_string":"Okayama University, Japan","institution_ids":["https://openalex.org/I163770644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019372108","display_name":"Jongseok Choi","orcid":null},"institutions":[{"id":"https://openalex.org/I4921948","display_name":"Pusan National University","ror":"https://ror.org/01an57a31","country_code":"KR","type":"education","lineage":["https://openalex.org/I4921948"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jongseok Choi","raw_affiliation_strings":["Pusan National University, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Pusan National University, Republic of Korea","institution_ids":["https://openalex.org/I4921948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101975138","display_name":"Howon Kim","orcid":"https://orcid.org/0000-0001-8475-7294"},"institutions":[{"id":"https://openalex.org/I4921948","display_name":"Pusan National University","ror":"https://ror.org/01an57a31","country_code":"KR","type":"education","lineage":["https://openalex.org/I4921948"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Howon Kim","raw_affiliation_strings":["Pusan National University, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Pusan National University, Republic of Korea","institution_ids":["https://openalex.org/I4921948"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5085541661"],"corresponding_institution_ids":["https://openalex.org/I3005327000"],"apc_list":null,"apc_paid":null,"fwci":1.9905,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.8930859,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"15","issue":"3","first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.8633345365524292},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.827669620513916},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.7564195990562439},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.624271810054779},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5161534547805786},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1428113579750061}],"concepts":[{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.8633345365524292},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.827669620513916},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7564195990562439},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.624271810054779},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5161534547805786},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1428113579750061},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2890502","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2890502","pdf_url":null,"source":{"id":"https://openalex.org/S136160450","display_name":"ACM Transactions on Embedded Computing Systems","issn_l":"1539-9087","issn":["1539-9087","1558-3465"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Embedded Computing Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.41999998688697815}],"awards":[],"funders":[{"id":"https://openalex.org/F4320335489","display_name":"Institute for Information and Communications Technology Promotion","ror":"https://ror.org/01g0hqq23"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W50929040","https://openalex.org/W141690682","https://openalex.org/W200116028","https://openalex.org/W275567227","https://openalex.org/W1490200949","https://openalex.org/W1567573409","https://openalex.org/W1573769949","https://openalex.org/W1580311733","https://openalex.org/W1607006990","https://openalex.org/W1649758727","https://openalex.org/W1870556762","https://openalex.org/W2004814164","https://openalex.org/W2009161425","https://openalex.org/W2043950313","https://openalex.org/W2052435632","https://openalex.org/W2129745589","https://openalex.org/W2146363265","https://openalex.org/W2151163104","https://openalex.org/W2156279885","https://openalex.org/W2200263712","https://openalex.org/W2203293987","https://openalex.org/W2486348220","https://openalex.org/W2582175223","https://openalex.org/W2915277450","https://openalex.org/W4302183993"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2090319426","https://openalex.org/W2036954759","https://openalex.org/W2057797376","https://openalex.org/W2506252583","https://openalex.org/W2048249848","https://openalex.org/W2260716361","https://openalex.org/W1987422982","https://openalex.org/W2029054571"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"present":[4],"a":[5],"hybrid":[6],"method":[7],"to":[8,63],"improve":[9],"the":[10,13,20,25,34,39,48],"performance":[11,84],"of":[12,19,51],"Montgomery":[14,26,36,54],"reduction":[15,27,37,55],"by":[16,86],"taking":[17],"advantage":[18],"Karatsuba":[21],"technique.":[22],"We":[23],"divide":[24],"into":[28],"two":[29],"sub-parts,":[30],"including":[31],"one":[32,41],"for":[33,42],"conventional":[35],"and":[38],"other":[40],"Karatsuba-aided":[43],"multiplication.":[44],"This":[45],"approach":[46],"reduces":[47],"multiplication":[49],"complexity":[50,65],"n":[52,58,61,68,72],"-limb":[53],"from":[56],"\u03b8(":[57],"2":[59,69],"+":[60,71],")":[62],"asymptotic":[64],"\u03b8":[66],"(7":[67],"/8":[70],").":[73],"Our":[74],"practical":[75],"implementation":[76],"results":[77],"over":[78],"an":[79],"8-bit":[80],"microcontroller":[81],"also":[82],"show":[83],"enhancements":[85],"11%.":[87]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
